FLC OF AN MLG ACR ACFT TOOK EVASIVE ACTION IN RESPONSE TO A TCASII RA AND INCREASED CLB RATE AND TURNED TO AVOID ANOTHER ACFT. NMAC.

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WE WERE FLT FROM BWI TO ROA. WE WERE HANDED OFF FROM BALTIMORE DEP TO ZDC. WE WERE CLRED TO FL200. WE WERE CLBING OUT OF 14500 FT WHEN THE TCASII SOUNDED A TA -- TFC; TFC. BOTH THE CAPT AND I LOOKED AT THE TCASII SCREEN AND NOTICED THE INTRUDER ACFT ON THE SCREEN AT 12 O'CLOCK AND APPROX 5 MI. BY THEN WE WERE AT 14700 FT AND REALIZED THE INTRUDER ACFT WAS AT 15000 FT. BEFORE THE TCASII RA; THE CAPT ADDED FULL PWR; TURNED 5 DEGS BANK TO R AND INCREASED CLB. WE THEN RECEIVED THE TCASII RA TO CLB; CLB. WE ESTIMATE THE TFC PASSED 300 FT HORIZ AND 300 FT VERT FROM OUR ACFT. WE WERE NEVER TOLD ANYTHING BY THE CTLR BEFORE THE TCASII RA. AFTERWARDS; THE CAPT QUERIED THE CTLR ABOUT THE TCASII RA. AFTER A SECOND CALL; THE CTLR SAID THE AIRPLANE WAS NORDO AT 15000 FT; AND THAT THE AIRPLANE PASSED BEHIND US. THE CAPT THEN INFORMED THE CTLR THAT HAD WE NOT HAD TCASII AND TURNED; THE TFC WOULD NOT HAVE PASSED US AT ALL. WE TOLD THE CTLR NO PROB AFTER HE APOLOGIZED. I DON'T KNOW IF THE CTLR WAS PREOCCUPIED WITH THE NORDO ACFT; OR WHAT; BUT THERE WAS A BREAKDOWN IN COM SOMEWHERE. WE SHOULD HAVE BEEN TOLD TO EXPEDITE CLB; OR STOP CLB AT 14000 FT. I CAN TELL YOU THIS; AT THE CLOSURE RATE AND OUR RATE OF CLB AT THE TIME; I FIGURE WE WOULD HAVE MISSED BY 50 FT OR NOT AT ALL IF WE HAD NOT HAD TCASII ON BOARD. THIS BEING MY FIRST RA; I AM A BELIEVER IN TCASII!